A variant of the classical Ramsey problem

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

For fixed integers p, q an edge coloring of a complete graph K is called a (p, q)-coloring if the edges of every Kp ⊆ K are colored with at least q distinct colors. Clearly, (p, 2)-colorings are the classical Ramsey colorings without monochromatic Kp subgraphs. Let f(n,p,q) be the minimum number of colors needed for a (p,q)-coloring of Kn. We use the Local Lemma to give a general upper bound for f. We determine for every p the smallest q for which f(n,p,q) is linear in n and the smallest q for which f(n,p,q) is quadratic in n. We show that certain special cases of the problem closely relate to Turán type hypergraph problems introduced by Brown, Erdos and T. Sós. Other cases lead to problems concerning proper edge colorings of complete graphs.

Original languageEnglish
Pages (from-to)459-467
Number of pages9
JournalCombinatorica
Volume17
Issue number4
Publication statusPublished - 1997

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Coloring
Colouring
Edge Coloring
Complete Graph
Erdös
Hypergraph
Color
Subgraph
Lemma
Upper bound
Distinct
Integer

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

A variant of the classical Ramsey problem. / Erdős, P.; Gyárfás, A.

In: Combinatorica, Vol. 17, No. 4, 1997, p. 459-467.

Research output: Contribution to journalArticle

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